Minimal error rate of linear, quadratic and logistic rules in discriminant analysis

A simulation study has been used to evaluate the minimal error rate of three affectation rules and to compare five estimators of this error rate for two groups of observations, in 480 situations characterized by the distribution and to the overlap of the populations, the number of variables, the sample size and the heteroscedasticity degree of the population under study. The results of this study suggest that the quadratic rule might be the best for heteroscedastic normal models. The linear rule showed better performance for homoscedastic normal or moderate non-normal models. The logistic rule is the best for severe non-normal models except when homoscedasticity occurs. As far as the comparison of five estimators is concerned, the results of the study indicate that eDS and eB are the best estimators of the minimal error rate for the linear rule, e5 for the quadratic rule and eD for the logistic rule.